Forrest Griffin pins down Quinton Jackson during the the UFC light heavy weight title bout in Las Vegas on Saturday. Photograph: Ronda Churchill/AP

In Las Vegas, anything is possible. Rollercoasters weave in and out of casinos, pop stars marry first, ask questions later and Elvis remains not only alive but capable of playing tens of different venues at the same time.

Yet even here certain things seem highly implausible. Upon hearing that the Ultimate Fighting Championship president Dana White had claimed that his event was going to become the biggest sport in the world, my first reaction was to laugh. Then I heard the kicker - he believes the UFC will get there within eight years.

"Delusional" is among the kinder verdicts to be found on mixed martial arts forums, not that such things faze White. "I don't just think it will be, I know it will be," he insisted at a low-key briefing for British journalists before UFC 86 on Saturday.

White's conviction is based on the fact that TV ratings for the UFC's top-rated shows are now competitive with some regular season NFL games in the United States, while the sport still has room for massive growth. The UFC's now regular shows in England are merely a signal of a far greater worldwide intent and White reasons that, while you might find people playing any number of different sports on any street corner in the world, all of them would drop what they were doing to watch a fight.

Given that the UFC's highest-rated show - UFC 75 - drew an average of 4.7 million viewers, while this year's Super Bowl had 97.5 million it will suffice to say that the onus remains on White to deliver rather more tangible evidence to support his argument. He specifically referenced football's World Cup as something the UFC could soon outdo yet even conservative estimates suggest the 2006 final was watched live by between 260 and 400 million people (the official figure released by Fifa was 715.1 million, but has been widely discredited).

But the fact White would even believe he could get away with such a statement is indicative of the way in which the UFC has consolidated itself as a mainstream sport over the past two years. The crowd at the Mandalay Bay Events Center may contain few families, but the city has been packed all weekend with kids nagging their parents for UFC merchandise.

The sight of three girls no older than 10 showing off T-shirts featuring one man kneeing another in the head to their proud fathers is likely to stay with me, yet White can justifiably argue that on many levels his athletes make great role models. The UFC, like Vegas, is brash, gaudy and loud in the way it presents itself but its fighters are often anything but. A tremendous value is placed on the respect of one's opponent, and it doesn't take a lot of exposure to the UFC's fighters to realise that they are unlike athletes in almost any other sport.

Unlike so often in boxing, there was not a hint of animosity between fighters at the weigh-in before UFC 86, despite attempts by a nearly 3,000-strong crowd to encourage it. When Quinton "Rampage" Jackson, the defending light-heavyweight champion and one of the sport's most renowned trash talkers, lost his belt to Forrest Griffin on a decision that several journalists disagreed with, the first words out of his mouth were not angry ones towards the officials but deferential ones towards his opponent. "He kicked my ass," he said, even mustering a smile.

The show itself is not everyone's cup of tea, and for all that organisers can rightfully be proud of the fact that a broken arm remains the UFC's worst ever injury, mixed martial arts remains an intensely violent sport. "I wouldn't let my kids watch it," says Evelyn, a mother who surprised her husband with tickets for his 40th birthday and for all the technical skill of the fighters, there is no denying that many in the sport's strongest demographic - males aged 18-34 - enjoy the adrenaline rush generated by such apparent brutality.

Indeed, fans consider themselves entitled to expect violence after shelling out as much as $650 (£330) face value for a ticket. This was the first UFC event I had attended in Vegas and the biggest difference I could discern was that the fans were even quicker to boo and heckle when fighters failed to live up to expectation. The fact that the show's overall production values were no higher than they have been in Britain was above all indicative of how seriously the UFC is taking international expansion.

Not that you could blame them. The UFC is now a serious money-making machine, and organisers have been quick to point out that merchandising sales at UK events comfortably outstripped those of music acts such as Girls Aloud and Take That at the same venues. White was elusive when I pushed him for clarification on whether his definition of being "bigger" than football revolved around viewing figures or revenue generated.

"I'll speak to you again in eight years," he smiled when I told him that either way, he is a long way from convincing me of his argument. It is a testament to how far the UFC has come that you don't doubt that it, and White will still be here come 2016, even if it will not have achieved quite the status he imagines.